1. Field of the Invention
This invention relates to temperature sensing with electrical devices, and more particularly to methods and apparatus for applying input signals to a semiconductor device and measuring temperature-dependent output signals from the device as an indication of temperature.
2. Description of the Prior Art
Numerous circuit devices, such as transistors, diodes and resistors, have operating characteristics that are temperature dependent. To accurately test a device to determine whether it is operating within prescribed limits, its temperature during the test procedure should accordingly be known. Because of its temperature dependence the device may itself be used as a temperature sensor, in which case it is especially important to determine whether it is operating accurately.
One approach to establishing a known relationship between the operating characteristics of a particular device and temperature is to immerse the device in a heated oil bath at a known temperature. Appropriate input and output signal readings are then taken to calibrate the device to the bath temperature. One disadvantage of using an oil bath is that it adds to the complexity, expense and time required for the testing process. Furthermore, even if the operating characteristics of a particular device are established for a particular bath temperature, its characteristics at all of the other temperatures of interest may not be accurately predictable from the information obtained.
Another approach to temperature measurement involves placing a calibrated thermometer in direct contact with the device or a substrate upon which it is formed, and continuing the contact long enough for the thermometer to reach the device or substrate temperature (typically several seconds). However, temperature variations within a substrate handler are generally too large to assume that each part is at the same temperature, and in any event it is difficult in practice to establish a satisfactory contact between the device or substrate and a thermometer. This approach also precludes the use of the device as a temperature sensor in its own right.
Since the operating characteristics of various devices are temperature dependent, it is at least conceptually possible to determine the device temperature by exciting an input signal to the device, observing a temperature-dependent output signal, and calculating the temperature from the relationship between the two signals. For example, germanium and silicon diodes have been operated at a constant forward-biased current and the resulting forward-biased voltage has been measured to determine the temperature in accordance with the standard forward-bias diode equation: ##EQU1## where V is the forward-bias voltage, k is Boltzmann's constant, q is the electron charge, T is the absolute temperature in degrees Kelvin, 1n is the natural logarithm function, I is the forward-bias current and I.sub.s is the diode's saturation current. Because of a strong temperature dependence of I.sub.s, V decreases rather than increases with temperature.
In practice the measurement of temperature with a diode is subject to several inaccuracies. The precise voltage-temperature relationship depends upon the actual details of the junction, notably the doping densities on either side of the junction, the dopant profiles and the junction area, as well as secondary considerations such as bulk and surface defects in the material. These factors are difficult to quantify with certainty, and many of the parameters in the device equations (such as mobility) are themselves temperature-dependent. Other effects such as conductivity modulation and series resistances can also complicate the device's behavior.
An improvement to the observation of current and voltage for a single junction involves the difference in forward-bias voltages of two separate junctions that are fabricated on the same substrate, but operated at different current densities. This eliminates the effects of variations in doping levels and in the value of the bandgap voltage. The technique is described, for example, in Timko, "A Two-Terminal IC Temperature Transducer", IEEE Journal of Solid-State Circuits, Vol. SC-11, No. 6, Dec. 1976, pages 784-788.
The dual junction approach has been implemented with a pair of bipolar transistors whose emitter areas are in the ratio A. The difference in collector current densities gives rise to a difference in the base-emitter voltages (V.sub.be) for the two transistors. The relationship between the base-emitter voltage differential and the device temperature is given by the expression: ##EQU2##
While the .DELTA.V.sub.be approach offers significant advantages over the single junction temperature measurement, it still has some limitations. There is a certain amount of tolerance in the transistor fabrication, which introduces an ambiguity into the emitter area ratio. Furthermore, the accuracy of the equation is reduced by ohmic resistances associated with the junction, specifically the base resistance r.sub.b and the emitter resistance r.sub.e. The base and emitter resistances may be considered to include both the internal resistances inherent in the device, and the resistances associated with connecting lines. Calibration of the temperature sensor is also required for most applications, and the fact that at least a pair of junctions are required introduces the possibility that differential strain across the substrate could result in poor tracking of junction voltages with a consequent error in the small difference voltage.